How are discontinuities and zeros determined in a rational function
1 answer:
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For 1 and 2, you plot both lines, and wherever they intersect is the solution to the system. Given the equation of a line, I think the easiest way to plot it is to find two points on the line, then draw a line through them. For example, if , then when
, you get
; when
, you get
. So plot the points (0, -1) and (1, 4), then strike a line through.
1. Notice that dividing both sides of by 2 returns
, same as the first equation. So the system of equations reduces to one equation, which can have an infinite number of solutions. (This is because for any choice of
or
, you can always find a corresponding value for the other variable.)
2. See attached image. is given by the purple line.
For 3-6, you have several options. The two simplest methods of solving them are by substitution or elimination.
3. Like with (1), notice that dividing both sides of the first equation by 2 gives , so there will be an infinite number of solutions.
4. (by substitution) Since , we can replace
in the second equation:
but this is false, so there are no solutions to this system.
5. (by substitution) Since , in the first equation we have
Then back in the second equation we find
So (-4, -3) is the only solution here.
6. (by substitution) Notice that the left hand sides of both equations are the same, so we end up with 7 = 12, but this is false, so no solution exists.
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The correct option is A.
<h3>What is a triangle?</h3>A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
The length of different sides are:
Since the length of all the sides of the triangle is not equal it is a scalene triangle.
Hence, the correct option is A.
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